About 21,800 results
|When e = 0, the sine-Gordon equation is completely integrable. Usually in partial |
differential equations one can only study the stability of a few very simple
solutions; however, for these integrable wave equations, a representation due to
|Later Kolmogorov, Arnold, and Moser showed that certain qualitative properties |
of completely integrable systems persist after perturbation: certain ... More
recently it has been shown that certain nonlinear partial differential equations
such as ...
|The idea of the proof of the sufficiency of the conditions stated in the theorem is to |
show that these guarantee that each of the M1- and M2-characteristic systems C(I
,dM 1) and C(I,dM 2) has a completely integrable subsystem of rank three.
|Many of the important local properties of surfaces are expressed in terms of |
partial differential equations, a famous example being ... which is one of the
prototypical examples of a completely integrable non-linear partial differential
|a nonlinear ordinary differential equation is the uniformizability of its general |
solution. ... In the Lax pair method one usually asserts that a system of partial
differential equations is completely integrable if it can be deduced as the
Peter J. Vassiliou, Ian G. Lisle - 2000 - Preview
|be completely integrable. By iterating this construction, we obtain a flag of C°(Mn, |
R)-modules ... c 1(*) c... c 1(1) c I, (5) where I(*) is defined recursively by 1(k) = (1(
k-1))(1). The flag (5) is called the derived flag of T. It stabilizes at a C°(Mn, ...
|By restricting to the case N = 1, we recover the elliptical representation of Heun's |
differential equation (see (4.3)). It is known that the Inozemtsev model of type
BCN is completely integrable. Namely, there exist N differential operators P1(= H)
|Therefore, the system of equations (3) will be completely integrable if and only if |
the single differential equation dz = (J) dx + \j/ dy i.e., §dx + \\fdy-dz = 0 ...(4) is
integrable. We know that the necessary and sufficient condition for the single ...
|In other words, the forms 1 (t),..., n(t) satisfy the linear ordinary differential |
equations (1.9). ... that a distribution P is completely integrable if for any point a ∈
M there exists an integral manifold N of P such that a ∈ N and dim N = dim P.
|Volume 23, 1g86 ON COMPLETELY INTEGRABLE SYSTEMS WITM MIGMER |
OR0ER CORRECTIONS Yuji Kodama ABSTRACT. The integrable Mamiltonian
systems with certsin claas of perturbations such as higher order corrections are ...